Generalized exterior sphere conditions and $\varphi$-convexity

Chadi Nour; Ron J. Stern; Jean Takche

doi:10.3934/dcds.2011.29.615

Article Contents

2011, Volume 29, Issue 2: 615-622. Doi: 10.3934/dcds.2011.29.615

This issue Previous Article Generalized solutions to nonlinear stochastic differential equations with vector--valued impulsive controls Next Article $V$-Jacobian and $V$-co-Jacobian for Lipschitzian maps

Generalized exterior sphere conditions and $\varphi$-convexity

1.
Computer Science and Mathematics Division, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos
2.
Department of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8
3.
Department of Computer Science and Mathematics, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos

Received: July 31, 2009

Revised: February 28, 2010

Published: May 2011

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Abstract

We consider sets $S\subset\R^n$ satisfying a certain exterior sphere condition, and it is shown that under wedgedness of $S$, it coincides with $\varphi$-convexity. We also offer related improvements concerning the union of uniform closed balls conjecture.

Keywords:

$\theta$-exterior sphere condition,
$\varphi$-convexity,
wedgedness,
$\psi$-semiconcavity,
union of uniform closed balls conjecture,
proximal analysis,
nonsmooth analysis.

Mathematics Subject Classification: Primary: 49J52; Secondary: 52A20.

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